There are n pieces arranged in a line, and each piece is colored either by 'A' or by 'B'. You are given a string colors of length n where colors[i] is the color of the ith piece.
Alice and Bob are playing a game where they take alternating turns removing pieces from the line. In this game, Alice moves first.
\n\n'A' if both its neighbors are also colored 'A'. She is not allowed to remove pieces that are colored 'B'.'B' if both its neighbors are also colored 'B'. He is not allowed to remove pieces that are colored 'A'.Assuming Alice and Bob play optimally, return true if Alice wins, or return false if Bob wins.
\n
Example 1:
\n\n\nInput: colors = "AAABABB"\nOutput: true\nExplanation:\nAAABABB -> AABABB\nAlice moves first.\nShe removes the second 'A' from the left since that is the only 'A' whose neighbors are both 'A'.\n\nNow it's Bob's turn.\nBob cannot make a move on his turn since there are no 'B's whose neighbors are both 'B'.\nThus, Alice wins, so return true.\n\n\n
Example 2:
\n\n\nInput: colors = "AA"\nOutput: false\nExplanation:\nAlice has her turn first.\nThere are only two 'A's and both are on the edge of the line, so she cannot move on her turn.\nThus, Bob wins, so return false.\n\n\n
Example 3:
\n\n\nInput: colors = "ABBBBBBBAAA"\nOutput: false\nExplanation:\nABBBBBBBAAA -> ABBBBBBBAA\nAlice moves first.\nHer only option is to remove the second to last 'A' from the right.\n\nABBBBBBBAA -> ABBBBBBAA\nNext is Bob's turn.\nHe has many options for which 'B' piece to remove. He can pick any.\n\nOn Alice's second turn, she has no more pieces that she can remove.\nThus, Bob wins, so return false.\n\n\n
\n
Constraints:
\n\n1 <= colors.length <= 105colors consists of only the letters 'A' and 'B'Compiled with clang 11 using the latest C++ 17 standard.
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